This money will go to "smaller, viable, credit worthy firms hit by the downturn," said Lord Mandelson. These companies will be able to borrow a maximum of £1m, with 75% guaranteed by the government. The money can be used for working capital - to pay wages for example - or for new investment, he said.
The banks must certify that these loans are in addition to loans that they would otherwise make.
Finally, the government is setting up a £75m Capital for Enterprise Fund specifically for businesses with high levels of debt that have "exhausted traditional forms of financing", said Lord Mandelson.
Fifty million pounds will be provided by the government and £25m by the major banks.
Lord Mandelson also said that the government was in discussions with credit insurance providers about providing similar guarantees on money owed by small businesses to their suppliers.
"Businesses are critically in need of cash-flow. Any move to get banks lending again will be seen as good news at this bleak time," said the British Chamber of Commerce's director-general David Frost.
"A government promise to guarantee individual loans to businesses is not only sensible, it's crucial."
However, some commentators believe that larger guarantees will be needed.
We have agreed credit again but it was hard fought - we fought tooth and nail to get it. It is very difficult.
Jeyson Flegg Flegg Transport, Aylesbury, Bucks
"Twenty billion pounds is not a very large number in the context of the problem. I would be a lot happier if the scheme was a lot larger," said Jon Moulton, managing partner of private equity firm Alchemy Partners.
Martin Weale at the Institute of Economic and Social Research said: "It's been clear for months that something like this is needed. I'm not sure it is on an adequate scale.
"My guess is that it won't be enough. After a few months it will look like another of the government's half measures."
"This is a useful contribution but it won't fix the problem," said BBC business editor Robert Peston.
Shadow chancellor George Osborne said the government appeared to be offering a belated version of the £50bn scheme floated by the Tories several weeks ago.
"Let us hope that they will properly implement this Conservative policy rather than a pale imitation, or else they run the risk of repeating the mistakes of their expensive temporary VAT cut and achieving nothing," he said.
Liberal Democrat Treasury spokesman Vince Cable said: "The government should stop messing around with stunts and wheezes and ensure that the banks owned or part-owned by taxpayers operate as state banks maintaining lending for the economy."
The British Bankers Association, which represents the banks, said its latest data showed that in October and November, growth in lending to small businesses slowed towards the end of 2008, though it remained above 2007 levels.
Business leaders have said that the lack of available finance has played a part in the downturn of the UK economy, which the British Chambers of Commerce (BCC) described as a "frightening deterioration" towards the end of 2008.
Separate data from Equifax found that the number of business failures in 2008 was 18.2% higher than in 2007.
In another development, the chairman of Standard Chartered Bank, Mervyn Davies, has been made a life peer and trade minister.
The BBC's Nick Robinson says he will, in effect, replace the ex-head of the Confederation of British Industry, Digby Jones, who left in the last cabinet reshuffle.
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